President Trump's performance at the G-20 summit in Germany produced a wave of commentary claiming the United States has abdicated its role as world leader.

ABC News contemplated "A World Without U.S. Leadership." CNN reported that Trump exchanged "an aggressive, traditional American leadership role for isolation in a club of one." The liberal activist Neera Tanden tweeted, "Can we just admit that the era of American global leadership is over under Trump?"

The talking point quickly became conventional wisdom in Europe. In the UK, the Independent wrote, "The G-20 proves it. Because of Trump, the world no longer looks to America for leadership."

While there were disagreements in Hamburg between Trump and the other 19 nations on lots of things, including trade, the main factor in all the end-of-American-leadership talk was the president's decision to pull out of the Paris Climate Accord.

The idea is that, by not going along with the other 19 nations -- Argentina, Australia, Brazil, Canada, China, France, Germany, India, Indonesia, Italy, Japan, Mexico, Russia, Saudi Arabia, South Africa, South Korea, Turkey, the United Kingdom, and the European Union -- the United States is no longer leading.

In other words: One can only lead by following the group.

It's an odd formulation, reminiscent of the old Barack Obama "leading from behind" jokes, but it's the principle underlying the end-of-American-leadership talk. And it's not working with some of the president's key supporters on Capitol Hill.

"I'm glad that President Trump cares more about electricity rates in Paris, Arkansas than he does the Paris Climate Accord," Arkansas Republican Sen. Tom Cotton said in a text exchange Sunday. "Hollow agreements aside, the United States will continue to lead the world in environmental protection, while also exporting oil and gas abroad. In particular, American global energy dominance will help break Europe's dependence on Russian oil and gas, if only Germany would stop posturing at one moment, while cozying up to Putin in the next."

Indeed, it seems safe to say that as the U.S. further develops its energy output, it will also achieve its own voluntary emissions goals for 2020 and beyond. (Each country in the non-binding Paris deal got to set its own.) But if Trump sticks with his decision, the U.S. will not take part in the vast, billions-and-billions-of-dollars global wealth-redistribution system that is part of the Paris Agreement.

It was of course well known ahead of time that the other G-20 leaders opposed Trump's move. The question in Hamburg was what they would say about it in a formal statement. The Guardian reported that "tensions ran particularly high between French and U.S. officials," who fought over whether the final G-20 statement would include a mention of the U.S. helping other countries "to access and use fossil fuels more cleanly and efficiently." (It did.)

At the same time, Trump's decision made the other countries want to showcase the depth of their commitment to the Paris deal. "We take note of the decision of the United States of America to withdraw from the Paris Agreement," the G-20 leaders' final declaration said. Then: "The leaders of the other G-20 members state that the Paris Agreement is irreversible."

To American ears, the "irreversible" part sounded a little strange. In the context of government, what does "irreversible" mean? Americans, like all other humans, reverse things all the time. Even the Constitution can be amended. But the Paris Agreement -- which former President Obama imposed by executive authority without seeking the approval of the Senate in the normal treaty process -- that is "irreversible"?

And even for the G-20, what does "irreversible" mean? It certainly does not mean "inflexible." The 19 leaders noted that they are "moving swiftly towards its full implementation in accordance with the principle of common but differentiated responsibilities and respective capabilities, in the light of different national circumstances." In other words, in a non-binding agreement like Paris, individual countries can do what they gotta do.

That, according to the commentators, is the definition of leadership. Donald Trump chose to take the United States on a different course, which according to the same commentators is the abdication of leadership.

In an alternate universe, one could imagine analysis of Trump's European trip noting that the president is in fact leading -- leading, for example, in the defense of Western values. Bob Dole, the former Republican presidential candidate and senator, said just that, praising Trump for restoring "proud and strong American leadership" and helping "restore our position as leader of the free world."

But Dole, and Cotton, and other Trump supporters don't see leadership in the same way as the critics. For Trump's opponents, at least as far as the G-20 is concerned, leading is following, and following is leading.